Abstract: A drilling unit on a deck of a floating vessel, includes a drill tower structure with a heave-compensation system, a winch mounted at or near the deck, a crown block mounted at a top side of the drill tower structure and at least one wire rope between the winch and the crown block. The heave-compensation system includes a slideable support frame configured to be moved in a direction substantially parallel to the axial direction of the drill tower structure. Either the winch or the crown block is positioned within the slideable support frame such that a distance between the winch and the crown block is controlled by at least one electric motor or linear actuator. In an alternative embodiment in which a crown block in not employed, the winch is placed in the slideable support frame at the top side of the drill tower structure.